AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES Park Jong-Jin; Zhang Yong;
We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on , then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in  is not true.
average shadowing property;-average-pseudo-orbit;shadowing property(pseudo orbit tracing property);-pseudo-orbit;chain recurrent;